Mathematics

Mathematics

Problem

Let f(x)={x2−4,x≤24x−8,x>2f(x)= \begin{cases} x^{2}-4, & x\le 2\\ 4x-8, & x>2 \end{cases} Determine whether there exists a number cc in [0,3][0,3] such that f(c)=0f(c)=0. Answer "exists" or "does not exist" and support your conclusion with the appropriate endpoint values.

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